understanding the underlying paper

[paulGitHub01]

I am currently working on my master's thesis in the area of "linear spin wave theory for RIXS" and have been revisiting the calculations presented in the paper "Linear spin wave theory for single-Q incommensurate magnetic structures" that SpinW is based on.

While reproducing the results, I encountered a discrepancy in Equation 47. In my calculations, the positions of the T and T^+ matrices, as well as the V and Z matrices, appear to be swapped compared to the expression in the paper. I have attached my derivation and the equation 47 from teh paper for reference and explanation.

I would be very grateful if someone could help me understand where this discrepancy might come from.

equation from the paper:

my derivation:

[RichardWaiteSTFC]

Hi @paulGitHub01 - thanks for getting in touch.
There is some developer documentation in the progress of being written (to help with conversion from MATLAB to python)
https://github.com/SpinW/pySpinW/blob/30480f3b991366f126ddef111b589694db84eda9/docs/developers/design/001_linear_spinwave_theory.md
I think @mducle, @lucas-wilkins or @alexhroom who have been working on this documentation would be interested in this.